Formation of Routh's Array in the Presence of a Row of Zeroes

Abstract

While forming Routh's Array used for the determination of the stability of a system, it is sometimes advantageous to introduce an inflnitesimally small shift of the imaginary axis- This can avoid a situation resulting in a row of zeroes, since it introduces asymmetry.

This method is also useful in using Routh-Hurwitz criterion to find out the root distribution correctly in the left-hand plane (LHP), on the imaginary axis and in the right-hand plane (RHP).

An algorithm is developed for forming the array taking the first-order approximation only.

Indexing Terms:

• Routh's Array
• System Stability